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What to do when you haven’t got a clue. Terry A. Ring Chem. Eng. University of Utah www.che.utah.edu/~ring/Statistically Designed Experiments. My First Job. Al 2 O 3 Powder. Water spray. My First Task Process that I knew nothing about. Nodulization Drying Sintering Plant - PowerPoint PPT Presentation
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What to do when you haven’t got a clue.
Terry A. RingChem. Eng.
University of Utahwww.che.utah.edu/~ring/Statistically Designed Experiments
My First Job
• My First Task• Process that I
knew nothing about.– Nodulization– Drying– Sintering
• Plant– 3m (0.5m tall)
• Pilot Plant– 1m(0.3m tall)
Conveyor Belt
ShaftKiln
1800C
Water spray
Drying Oven
Al2O3 Powder
Process
• Problem– Control Ball Size
– Minimize H2O
– Minimize Pore Volume
– Low Dust Emissions
• 6 mo. to solve problem
Conveyor Belt
ShaftKiln
1800C
Water Spray
Drying Oven
3 cm
2.5 cm
Al2O3 powder
Variables
• Variables– Water flow rate
• Concentration of additives
– Powder Flow Rate– RPM– Time in Dryer– Temp Dryer– Time in Shaft Kiln– Temp of Shaft Kiln
• 6 mo. to solve problem
Conveyor Belt
ShaftKiln
1800C
Water Spray
Drying Oven
3 cm
2.5 cm
Al2O3 powder
What to do?
• Literature Review on Nodulization– 1 paper– 1 PhD thesis
– m(d,t) is the mass of sphere of diameter d
• How do I solve this?• What do I do now?
V
tdmQtdmddkdxtxm
e
edxk
dt
tddm kkk
bo
xdb
o
),(),()/(),(]
1
1[)/(
),(1
/
0
Now what do you do?
• Get Help– Plant Operator in Baton Rouge, Louisiana
• Nothing Useful
– Technician that last ran the Pilot Plant• Water flow rate seemed to be critical.
– Talk to others at the research site• Idea at lunch to use statistically designed
experiments– Consultant gave lecture 2 years ago at site.
Statistically Designed Experiments
• Save time and money
• Find out what variables are important– Tell you if you have all the important variables– Tell you if some variables are not important– Tell you if variable interact
• Non-linear effects
• Gives a Model for prediction purposes
• Allows optimization of the process
Used today in
• Pharma– Drug Development
• Silicon Chip Processing– From Wafers to chips
• It is the basis of 6 sigma’s statistical process analysis
Traditional Experimentation
• Move one variable at a time• Keep other variables constant• No of experiments = LV
– V=Variables– L=Levels
• Traditional Experimentation– 57=78,125 experiments– 37=2,187 experiments– Need to reduce the number of variables
Levels of x2
y Response
Saves Time and Money
• No of experiments = LV
– V=Variables– L=Levels
• Traditional Experimentation– 53=125 experiments
• Statistically Designed Experiments• 23= 8 experiments + 2 (repeats)=10 expts.• 23= 8 experiments x 2 (repeats)=16 expts.
– Vary all variables simultaneously then mathematically sort things out
Levels of x2
yi Response
Process for Design of Experiments
• Select Variables – RMP, Water Flow, Drying Time, Sintering Time
• Select range of to manipulate the variables– Low value (-) sometimes scaled variable -1– High value (+) sometimes scaled variable +1
• Select Measurements to be made– Ball Diameter, Pore Volume, H2O content,
Dust
• Run Experiments in a Randomized Order
Variables for 23 Design
Mathematics
• Calculate Effects of each variable on each measurement
• Ei=Σyi(+)- Σyi(-)
• Prediction Equation• y(x)=E1x1+ E2x2+ E3x3+ …• E1E2x1x2+ E1E3x1x3+ E2E3x2x3+• E123 x1x2x3
• Generate Response Surface Map• Optimize
Response Surface Map
Various Software to do this
• ** Stat-ease from Stat-ease Inc. – (3 mo free license)
• DOE from BBN Software Products• Reliasoft• MiniTab• Statistica from Statsoft• DoE from Camo• Others
Why do you do experiments?
• Understand how process responds to changes in variables
• Develop a mathematical description of the process
• Verify a model– Determine various coefficients in the model
Physical Model vs DoE model
• Physics based Model– Often physics is too difficult to model– Often equations are too difficult to solve– Use of simplified model is all too often occurrence
• DoE Model– Little physical significance to Effects in equation– Good only inside box
• Minor extrapolation is possible
Use Physics to guide variable choice
• Suppose you know the physics behind the model– Choose a variable and response that are linearly related.
• Suppose we vary temperature and are looking at the output from a bleaching operation– Use 1/T as a variable– Use Cbleach as a variable– Use ln[whiteness] as measured response– This approach will determine the activation energy as the
temperature effect and the rate constant as the concentration effect.
– The standard errors will be determined giving the error on the activation energy and the rate constant.
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